# Documentation

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# spiralArchimedean

Create Archimedean spiral antenna

## Description

The `spiralArchimedean` object is a planar Archimedean spiral antenna on the X-Y plane. The Archimedean spiral is always center fed and has two arms. The field characteristics of this antenna are frequency independent. A realizable spiral has finite limits on the feeding region and the outermost point of any arm of the spiral. The spiral antenna exhibits a broadband behavior. The outer radius imposes the low frequency limit and the inner radius imposes the high frequency limit. The arm radius grows linearly as a function of the winding angle.

The equation of the Archimedean spiral is:

`$r={r}_{0}+a\varphi$`
where:

• r0 is the inner radius

• a is the growth rate

• ϕ is the winding angle of the spiral

Archimedean spiral antenna is a self complimentary structure, where the spacing between the arms and the width of the arms are equal. The default antenna is center fed. The feed point coincides with the origin. the origin is located in the X-Y plane.

## Creation

### Syntax

``sa = spiralArchimedean``
``sa = spiralArchimedean(Name,Value)``

### Description

``` `sa = spiralArchimedean` creates a planar Archimedean spiral on the X-Y plane. By default, the antenna operates over a broadband frequency range of 3–5 GHz.```

example

``` `sa = spiralArchimedean(Name,Value)` creates a planar Archimedean spiral, with additional properties specified by one, or more name–value pair arguments. `Name` is the property name and `Value` is the corresponding value. You can specify several name-value pair arguments in any order as `Name1`, `Value1`, `...`, `NameN`, `ValueN`. Properties not specified retain their default values.```

## Properties

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Number of turns of spiral, specified as a scalar.

Example: `'Turns',2`

Data Types: `double`

Spiral inner radius, specified as a scalar in meters.

Example: `'InnerRadius',1e-3`

Data Types: `double`

Outer radius of spiral, specified as a scalar in meters.

Example: `'OuterRadius',1e-3`

Data Types: `double`

Direction of spiral turns (wingdings), specified as `CW` or `CCW`.

Example: `'WindingDirection'`,`'CW'`

Data Types: `char`

Lumped elements added to the antenna feed, specified as a lumped element object handle. For more information, see `lumpedElement`.

Example: `'Load',lumpedelement`. `lumpedelement` is the object handle for the load created using `lumpedElement`.

Tilt angle of antenna, specified as a scalar or vector with each element unit in degrees.

Example: `'Tilt',90`

Example: `'Tilt',[90 90 0]`

Data Types: `double`

Tilt axis of the antenna, specified as:

• A three-element vector of Cartesian coordinates in meters. In this case, each vector starts at the origin and lies along the specified points on the X, Y, and Z axes.

• Two points in space as three-element vectors of Cartesian coordinates. In this case, the antenna rotates along the line joining the two points.

• A string input for simple rotations around the principal planes, X, Y, or Z.

Example: `'TiltAxis',[0 1 0]`

Example: `'TiltAxis',[0 0 0;0 1 0]`

Example: `'TiltAxis','Z'`

Data Types: `double`

## Object Functions

 `show` Display antenna or array structure; Display shape as filled patch `info` Display information about antenna or array `axialRatio` Axial ratio of antenna `beamwidth` Beamwidth of antenna `charge` Charge distribution on metal or dielectric antenna or array surface `current` Current distribution on metal or dielectric antenna or array surface `design` Design prototype antenna for resonance at specified frequency `EHfields` Electric and magnetic fields of antennas; Embedded electric and magnetic fields of antenna element in arrays `impedance` Input impedance of antenna; scan impedance of array `mesh` Mesh properties of metal or dielectric antenna or array structure `meshconfig` Change mesh mode of antenna structure `pattern` Radiation pattern of antenna or array; Embedded pattern of antenna element in array `patternAzimuth` Azimuth pattern of antenna or array `patternElevation` Elevation pattern of antenna or array `returnLoss` Return loss of antenna; scan return loss of array `sparameters` S-parameter object `vswr` Voltage standing wave ratio of antenna

## Examples

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Create and view a 2-turn Archimedean spiral antenna with a 1 mm starting radius and 40 mm outer radius.

```sa = spiralArchimedean('Turns',2, 'InnerRadius',1e-3, 'OuterRadius',40e-3); show(sa)```

Calculate the impedance of an Archimedean spiral antenna over a frequency range of 1-5 GHz.

```sa = spiralArchimedean('Turns',2, 'InnerRadius',1e-3, 'OuterRadius',40e-3); impedance(sa, linspace(1e9,5e9,21));```

## References

[1] Balanis, C.A. Antenna Theory. Analysis and Design, 3rd Ed. New York: Wiley, 2005.

[2] Nakano, H., Oyanagi, H. and Yamauchi, J. “A Wideband Circularly Polarized Conical Beam From a Two-Arm Spiral Antenna Excited in Phase”. IEEE Transactions on Antennas and Propagation. Vol. 59, No. 10, Oct 2011, pp. 3518-3525.

[3] Volakis, John. Antenna Engineering Handbook, 4th Ed. McGraw-Hill